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交错级数
∑n=1∞(−1)n−11n=ln2\sum_{n=1}^{\infty}(-1)^{n-1}\frac{1}{n}=ln2∑n=1∞​(−1)n−1n1​=ln2
证明：
limn→+∞S2nlim_{n\rightarrow+\infty}S_{2n}limn→+∞​S2n​=limn→+∞S2n+1lim_{n\rightarrow+\infty}S_{2n+1}limn→+∞​S2n+1​
S2n=1−12+13−14+⋯+12n−1−12n=1+12+13+⋯+12n−1+12n−2∗(12+14+⋯+12n)=1n+1+1n+2+⋯+12n−1+12n\begin{aligned}
S_{2n} &amp;= 1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots+\frac{1} {2n-1}-\frac{1}{2n} \\
       &amp;=1 ...</div></div></div><div class="recent-post-item"><div class="post_cover right"><a href="/2022/08/23/Mathjax%E4%BD%BF%E7%94%A8%E6%8C%87%E5%8D%97(%E4%B8%8D%E6%96%AD%E6%9B%B4%E6%96%B0)/" title="Mathjax使用指南(不断更新)"><img class="post_bg" src="/img/ani.png" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="Mathjax使用指南(不断更新)"></a></div><div class="recent-post-info"><a class="article-title" href="/2022/08/23/Mathjax%E4%BD%BF%E7%94%A8%E6%8C%87%E5%8D%97(%E4%B8%8D%E6%96%AD%E6%9B%B4%E6%96%B0)/" title="Mathjax使用指南(不断更新)">Mathjax使用指南(不断更新)</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">Created</span><time datetime="2022-08-23T08:27:02.000Z" title="Created 2022-08-23 16:27:02">2022-08-23</time></span></div><div class="content">公式块和行内公式的添加
1.公式块
hθ(x)=θ0+θ1xh_\theta(x)=\theta_0+\theta_1x
hθ​(x)=θ0​+θ1​x
2.行内公式
自变量θ增大，函数、θ2也同时增大自变量\theta增大，函数、\theta^2也同时增大自变量θ增大，函数、θ2也同时增大
常用符号的代码
1.上下标，正负无穷
x2x^2x2
y1y_1y1​
∞\infty∞
−∞-\infty−∞
2.加减乘，分式，根号，省略号
a+b−c∗da+b-c*da+b−c∗d
a÷ba\div{b}a÷b
a±ba\pm{b}a±b
ab\frac{a}{b}ba​
sqrt(b)sqrt{(b)}sqrt(b)
⋯\cdots⋯
3.三角函数
sin⁡θ\sin{\theta}sinθ
cos⁡θ\cos{\theta}cosθ
tan⁡θ\tan{\theta}tanθ
cot⁡θ\cot{\theta}cotθ
4.矢量，累加，累乘，极限
F⃗\vec{F}F
∑i=1nai\sum_{i=1}^n{a_i}∑i=1n​ai​
∏i=1nai\prod_{i=1}^{n}{a_ ...</div></div></div><div class="recent-post-item"><div class="post_cover left"><a href="/2022/08/04/%E6%8A%B1%E6%AD%89%EF%BC%8C%E5%AE%8B%E5%A8%9C/" title="抱歉，宋娜"><img class="post_bg" src="/img/4.png" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="抱歉，宋娜"></a></div><div class="recent-post-info"><a class="article-title" href="/2022/08/04/%E6%8A%B1%E6%AD%89%EF%BC%8C%E5%AE%8B%E5%A8%9C/" title="抱歉，宋娜">抱歉，宋娜</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">Created</span><time datetime="2022-08-04T08:02:51.000Z" title="Created 2022-08-04 16:02:51">2022-08-04</time></span></div><div class="content">抱歉，宋娜
我又闯入了你的世界
打扰了
8月4号，我又冲动了一回给你送花了
虽然我知道你很不想要，但是我还是硬着头皮给你了
本来，我是想给你唱一首歌的，最近学了电子琴，想着给你弹一首《月亮代表我的心》但是，我感觉这首歌太低级，等我电子琴学好一点再送给你，而且这也不能算是礼物吧，只能说我学会一首歌，也不是自己写的。
我等着你的消息，虽然我是下定决心要见你，但是真要见你，我心里真的紧张的要死。
我等着你的消息，我想着你要是直接非常斩钉截铁的拒绝我，那我真就躺平了。
我等着你的消息，你说，为什么要送花。
我找不到一个合适的理由，因为我不是你男朋友我不知道七夕节是要什么身份才能过是喜欢，还是要是男友，还是要是老公
不知道，我只想送你花，我向你表达的仅仅如此
因为我不敢向前迈开，我怕你的拒绝，我怕
借着隔壁的电动车，想着阿姨估计会说我了
想着又要借钱了，这个月买了电子琴本就没啥钱了，只能下个月注意点了
夏天炎热的风不禁让我想到很多事情，想着想着，然后花就包好了
说实话，感觉骑着电动车拿着一束花的场景真的很怪，有种乡下“土”豪的感觉。我知道路边的人在看，在浮想联翩，就如我一样但是我什么都不敢想，因 ...</div></div></div><div class="recent-post-item"><div class="post_cover right"><a href="/2022/05/03/%E4%BD%A0%E5%88%B0%E5%BA%95%E8%A6%81%E5%81%9A%E4%BB%80%E4%B9%88/" title="你到底要做什么"><img class="post_bg" src="/img/Mikasa.png" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="你到底要做什么"></a></div><div class="recent-post-info"><a class="article-title" href="/2022/05/03/%E4%BD%A0%E5%88%B0%E5%BA%95%E8%A6%81%E5%81%9A%E4%BB%80%E4%B9%88/" title="你到底要做什么">你到底要做什么</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">Created</span><time datetime="2022-05-03T08:02:35.000Z" title="Created 2022-05-03 16:02:35">2022-05-03</time></span></div><div class="content">我觉得可能真得思考自己想要什么了，整天浑浑噩噩过日子，不知道自己真正想要什么我觉得我不是一个可以抛下所有的人。
但是我确实想做好一件事可是我是一个不愿干忍受寂寞的人，我是一个热烈的人，恶心的想要烈酒的那种人。
可是也许只有寂寞才能塑造一个真正的英雄。可能我的一生注定要在寂寞中实现自我。
也许只要有一段回忆就已经足够了，生活中不让我们自己尽情挥洒，但是我们都有幸福的尺度。
我应该怎么做，自己心里清楚吗？读博吗？成为一个在科研中实现自我的人，还是在日常的工作中，找到真正的自我。
我觉得走一步看一步有时并没有什么错，但前提是你走得够快，足以快到看到自己的未来。
很多时候，我们都看不到自己的未来。所以也许我该速度一些，看到自己的未来。
</div></div></div><div class="recent-post-item"><div class="post_cover left"><a href="/2022/03/30/%E6%88%91%E8%A6%81%E6%80%8E%E4%B9%88%E5%8A%9E/" title="我要怎么办"><img class="post_bg" src="/img/3.png" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="我要怎么办"></a></div><div class="recent-post-info"><a class="article-title" href="/2022/03/30/%E6%88%91%E8%A6%81%E6%80%8E%E4%B9%88%E5%8A%9E/" title="我要怎么办">我要怎么办</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">Created</span><time datetime="2022-03-30T08:02:15.000Z" title="Created 2022-03-30 16:02:15">2022-03-30</time></span></div><div class="content">我认为我放下了，可是当我闲下来时，她仍然在我的脑海中。
我是不是要去找一个女朋友，消散一下曾经的感觉，彻底消散曾经的感觉。
我不知道，但是我肯定她谈了那么多的男朋友，说她对我的感觉还存在估计也是自欺欺人吧。
我不知道该做什么，闷下头来学习，感受到的内心的焦躁和不安。
似乎有她在，我可以盲目的自信，没有她在，我变得得过且过。
如果这个世界不存在永恒的爱，那么爱情又有什么意义呢我突然无法理解自己，明明想放手的是自己，留恋的也是自己。可能就是这样的我，真的不值得被爱吧。
可能只有忙能让我成为自己。我就应该忘记，善于忘记可是我一直不是一个麻木的人，我有自己的价值观，真的该死的价值观
现在我的状态是非常糟糕的，明天开始一定要忙起来，做好自己的事
如果我现在还有勇气和盲目的自信该有多好啊
抱着不怕受伤的心情去再一次接近她，但是我也忽略了对她的伤害，所以还是不要找她比较好吧。
</div></div></div><div class="recent-post-item"><div class="post_cover right"><a href="/2022/03/08/%E5%9C%A8%E6%B2%A1%E5%BE%97%E9%80%89%E6%8B%A9%E7%9A%84%E6%97%B6%E5%80%99%EF%BC%8C%E5%81%9A%E5%A5%BD%E8%AF%A5%E5%81%9A%E7%9A%84%E4%BA%8B%E6%83%85/" title="在没得选择的时候，做好该做的事情"><img class="post_bg" src="/img/Mikasa2.png" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="在没得选择的时候，做好该做的事情"></a></div><div class="recent-post-info"><a class="article-title" href="/2022/03/08/%E5%9C%A8%E6%B2%A1%E5%BE%97%E9%80%89%E6%8B%A9%E7%9A%84%E6%97%B6%E5%80%99%EF%BC%8C%E5%81%9A%E5%A5%BD%E8%AF%A5%E5%81%9A%E7%9A%84%E4%BA%8B%E6%83%85/" title="在没得选择的时候，做好该做的事情">在没得选择的时候，做好该做的事情</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">Created</span><time datetime="2022-03-08T08:01:14.000Z" title="Created 2022-03-08 16:01:14">2022-03-08</time></span></div><div class="content">感觉自己还是没有全身心投入，还是被窗外的风景所吸引。
到底要怎么办，才好。
因为我是一个活生生的人，我有好多欲望而不能专注一个欲望。
我竟然在想要不要祝她生日快乐，我竟然在想那么多的事情。
我竟然还喜欢看高木同学，是不是傻，你应该不会拥有那样的女孩了。
毁灭吧，只做好一件事吧，目前，你没得选择。
</div></div></div><div class="recent-post-item"><div class="post_cover left"><a href="/2022/03/05/%E8%AF%B7%E4%B8%93%E6%B3%A8%EF%BC%8C%E5%81%9A%E8%87%AA%E5%B7%B1/" title="请专注，做自己"><img class="post_bg" src="/img/Mikasa3.png" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="请专注，做自己"></a></div><div class="recent-post-info"><a class="article-title" href="/2022/03/05/%E8%AF%B7%E4%B8%93%E6%B3%A8%EF%BC%8C%E5%81%9A%E8%87%AA%E5%B7%B1/" title="请专注，做自己">请专注，做自己</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">Created</span><time datetime="2022-03-05T08:00:52.000Z" title="Created 2022-03-05 16:00:52">2022-03-05</time></span></div><div class="content">感觉自己还是没有克服一些不好的习惯，还是经常看自媒体视频，确实耽误了很多时间。
可是，猛地一下发现我的生活竟是这样的无趣。
我似乎有目标，但是却不愿意付出所有的努力，这样是不行的哦
要想做到自己理想的状态，就必须付出，就必须坚持。
相信自己，可以做到，静下心来，好好思考。
如果再不好好做自己，真的会后悔很久的。
我知道只学习真的比较无趣，所以你必须在其中寻找乐趣不是吗
你一直在想人为什么而活在这个世上，就目前而言，我想成为一个优秀的人。
不仅仅是为了别人的赞赏，而是为了自己内心的从容和淡然。
</div></div></div><div class="recent-post-item"><div class="post_cover right"><a href="/2022/03/01/%E7%9C%9F%E7%9A%84%E5%BE%97%E6%8B%BC%E4%B8%80%E4%B8%8B/" title="真的得拼一下"><img class="post_bg" src="/img/bingzhang.png" onerror="this.onerror=null;this.src='/img/404.jpg'" alt="真的得拼一下"></a></div><div class="recent-post-info"><a class="article-title" href="/2022/03/01/%E7%9C%9F%E7%9A%84%E5%BE%97%E6%8B%BC%E4%B8%80%E4%B8%8B/" title="真的得拼一下">真的得拼一下</a><div class="article-meta-wrap"><span class="post-meta-date"><i class="far fa-calendar-alt"></i><span class="article-meta-label">Created</span><time datetime="2022-03-01T08:00:33.000Z" title="Created 2022-03-01 16:00:33">2022-03-01</time></span></div><div class="content">感觉自己这个成绩，真的保研可能真心不太行，除非我能拿到CSP400，大英竞赛一等奖，才能保到理想的学校。
但是目前，我真心还没有考研的打算，所以可以再拼一次。
CSP拿到400分也许没有想象中的那么难，首先得有耐心，也就是心态必须要稳，其次必须有足够的熟练度大学英语竞赛可能拿到个全国二等经就不错了。
大创项目的话，得好好想想有没有晋升国家级的情况，如果做的好的话其实是有可能的。
所以真的得全力拼一下才知道自己能不能达得到。加油
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